Heat a large pan over medium-high heat. Add just enough vegetable oil to coat the bottom of the pan, and then brown the wontons in the oil, using tongs to turn them. They don’t need to be browned on all sides; just give them some color. Remove the browned wontons from pan and set aside.
Whisk eggs together in a small measuring cup with a pour spout. Set aside.
Add the chicken broth, soy sauce, and sesame oil to a large, heavy saucepan. Heat over medium-high. As the liquid heats up, use a wooden spoon to check the flavor of the soup base. Season to taste with additional soy sauce and sesame oil as needed. You may even want to throw in a pinch or two of sugar, depending on the kind of soy sauce you use. (As mentioned previously, the kind of soy sauce you use can dramatically change the flavor profile of the soup base.)When the soup base suites your tastes, bring it to a full, rolling boil.
Slowly pour beaten eggs in a thin stream into boiling liquid. Eggs will cook on contact.
Reduce the heat until the soup base is at a steady, hard simmer.SLOWLY begin pouring the beaten eggs in a thin stream into boiling liquid. The eggs will cook into ribbons on contact.
When all the eggs are cooked, add the prepared dumplings and sliced green onions to the hot soup base. Frozen Wontons: Add frozen wontons to liquid one at a time, and heat until liquid has returned to a simmer. Cook wontons for 5-6 minutes after broth has returned to a simmer.Browned Wontons: Add browned wontons to liquid all at once, and heat until liquid has returned to a simmer. Cook wontons for 2-3 minutes after broth has returned to a simmer.
When the soup is done, serve it up in bowls with some tamari, shoyu, or soy sauce on the side; along with whatever else you like to use to spice up your soup. Garnish with additional sliced green onions.
Notes
When adding eggs to hot soup base:If you stir the boiling soup base as you add the eggs, they will break up and break into smaller, thinner ribbons. I prefer to not stir the soup base as it simmers, which in turn produces larger, slightly thicker ribbons of beaten egg.